Results 201 to 210 of about 466,993 (231)
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1970
In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
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In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
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2016
In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
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In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
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On a random Volterra integral equation
Mathematical Systems Theory, 1973Tsokos [12] showed the existence of a unique random solution of the random Volterra integral equation (*)x(t; ω) = h(t; ω) + ∫ k(t, τ; ω)f(τ, x(τ; ω)) dτ, whereω ∈ Ω, the supporting set of a probability measure space (Ω,A, P)
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Integral Equations of Volterra Type
2010In this article we will try to give a review of certain aspects of the current state of the qualitative theory of Volterra integral and integrodifferential equations. It should be apparent from the other articles in this volume that such equations do occur in biological applications and hence we will not worry about the raison d'etre of this theory ...
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Volterra-Fredholm Integral Equations
2011The Volterra-Fredholm integral equations [1–2] arise from parabolic boundary value problems, from the mathematical modelling of the spatio-temporal development of an epidemic, and from various physical and biological models. The Volterra-Fredholm integral equations appear in the literature in two forms, namely $$u\left( x \right) = f\left( x \right)
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Nonlinear Volterra Integral Equations
2011It is well known that linear and nonlinear Volterra integral equations arise in many scientific fields such as the population dynamics, spread of epidemics, and semi-conductor devices. Volterra started working on integral equations in 1884, but his serious study began in 1896. The name integral equation was given by du Bois-Reymond in 1888.
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